

from __future__ import annotations

from typing import Any







class 					__lowercase  :





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase    ,						__UpperCAmelCase = 0						)		->       None:
														A		,		A      :					Optional[int]      		=					row, column
														A      :					Optional[Any]      		=					[[default_value for c in range(__UpperCAmelCase						)] for r in range(__UpperCAmelCase						)]




							def __str__(					self						)		->       str:
														A      :					List[str]      		=					f'Matrix consist of {self.row} rows and {self.column} columns\n'

														# Make string identifier
														A      :					Dict      		=					0
														for row_vector in self.array:
																					for obj in row_vector:
																												A      :					Dict      		=					max(__UpperCAmelCase    ,						len(str(__UpperCAmelCase						)						)						)
														A      :					Any      		=					f'%{max_element_length}s'

														# Make string and return
														def single_line(__UpperCAmelCase						) -> str:
																					nonlocal string_format_identifier
																					A      :					List[str]      		=					'''['''
																					line += ", ".join(string_format_identifier % (obj,) for obj in row_vector						)
																					line += "]"
																					return line

														s += "\n".join(single_line(__UpperCAmelCase						) for row_vector in self.array						)
														return s




							def __repr__(					self						)		->       str:
														return str(self						)




							def       snake_case			(					self    ,						__UpperCAmelCase						)		->       bool:
														if not (isinstance(__UpperCAmelCase    ,						(list, tuple)						) and len(__UpperCAmelCase						) == 2):
																					return False
														elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
																					return False
														else:
																					return True




							def __getitem__(					self    ,						__UpperCAmelCase						)		->       Any:
														assert self.validate_indicies(__UpperCAmelCase						)
														return self.array[loc[0]][loc[1]]




							def __setitem__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       None:
														assert self.validate_indicies(__UpperCAmelCase						)
														A      :					str      		=					value




							def __add__(					self    ,						__UpperCAmelCase						)		->       Matrix:
														assert isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						)
														assert self.row == another.row and self.column == another.column

														# Add
														A      :					Union[str, Any]      		=					Matrix(self.row    ,						self.column						)
														for r in range(self.row						):
																					for c in range(self.column						):
																												A      :					int      		=					self[r, c] + another[r, c]
														return result




							def __neg__(					self						)		->       Matrix:
														A      :					Tuple      		=					Matrix(self.row    ,						self.column						)
														for r in range(self.row						):
																					for c in range(self.column						):
																												A      :					List[str]      		=					-self[r, c]
														return result




							def __sub__(					self    ,						__UpperCAmelCase						)		->       Matrix:
														return self + (-another)




							def __mul__(					self    ,						__UpperCAmelCase						)		->       Matrix:

														if isinstance(__UpperCAmelCase    ,						(int, float)						):  # Scalar multiplication
																					A      :					str      		=					Matrix(self.row    ,						self.column						)
																					for r in range(self.row						):
																												for c in range(self.column						):
																																			A      :					List[str]      		=					self[r, c] * another
																					return result
														elif isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):  # Matrix multiplication
																					assert self.column == another.row
																					A      :					Any      		=					Matrix(self.row    ,						another.column						)
																					for r in range(self.row						):
																												for c in range(another.column						):
																																			for i in range(self.column						):
																																										result[r, c] += self[r, i] * another[i, c]
																					return result
														else:
																					A      :					Union[str, Any]      		=					f'Unsupported type given for another ({type(__UpperCAmelCase						)})'
																					raise TypeError(__UpperCAmelCase						)




							def       snake_case			(					self						)		->       Matrix:
														A      :					Tuple      		=					Matrix(self.column    ,						self.row						)
														for r in range(self.row						):
																					for c in range(self.column						):
																												A      :					Tuple      		=					self[r, c]
														return result






							def       snake_case			(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Any:
														assert isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						) and isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						)
														assert self.row == self.column == u.row == v.row  # u, v should be column vector
														assert u.column == v.column == 1  # u, v should be column vector

														# Calculate
														A      :					Optional[Any]      		=					v.transpose()
														A      :					Any      		=					(v_t * self * u)[0, 0] + 1
														if numerator_factor == 0:
																					return None  # It's not invertable
														return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":






		def        snake_case__		(    ):
									# a^(-1)
									A      :					Any      		=					Matrix(3     ,				3     ,				0		)
									for i in range(3		):
																A      :					int      		=					1
									print(F'a^(-1) is {ainv}'		)
									# u, v
									A      :					Union[str, Any]      		=					Matrix(3     ,				1     ,				0		)
									A		,		A		,		A      :					Union[str, Any]      		=					1, 2, -3
									A      :					Union[str, Any]      		=					Matrix(3     ,				1     ,				0		)
									A		,		A		,		A      :					Optional[int]      		=					4, -2, 5
									print(F'u is {u}'		)
									print(F'v is {v}'		)
									print(F'uv^T is {u * v.transpose()}'		)
									# Sherman Morrison
									print(F'(a + uv^T)^(-1) is {ainv.sherman_morrison(lowerCamelCase_     ,				lowerCamelCase_		)}'		)






		def        snake_case__		(    ):
									import doctest

									doctest.testmod()

		testa()









def        snake_case__		(    lowerCamelCase_ = 1000		):
							return sum(e for e in range(3     ,				lowerCamelCase_		) if e % 3 == 0 or e % 5 == 0		)


if __name__ == "__main__":
		print(F"{solution() = }")






